This framework is parsimonious, which allowed us to capture many of
the salient features of the data, and to partially account for movements
in the world market in a model with relatively few parameters. Later, we
would estimate a multivariate GARCH model that would allow us a richer
model of the joint dynamics of country-specific and world-market returns.
Following Pagan and Schwert (1990) and Engle and Ng (1993), the
first step in our univariate GARCH analysis was to remove from the time
series any predictability associated with lagged returns or day-of-the-week
effects. For each country, the following regression was estimated:

where Rt is the daily return on the country’s stock index and RWt is the
daily return on the World Market Index on day t, RWt1 is the lagged return on the World Market Index, and DAYj are day-of-the-week dummies
for Tuesday through Friday.
We used the excess return relative to the World Market Index as our
dependent variable and the lagged World Market Index return as an independent
variable in an effort to remove the effect of worldwide price
movements on volatility.6 It should be noted that because of differences
in time zones, different markets line up differently with the world-market
return. This makes it difficult to compare directly the coefficients of the
first-stage regression. For example, if the U.S. market is influenced by
Asian markets, this will be reflected through the contemporaneous market
return on the left-hand side of the regression equation. On the other
hand, if the Asian markets are influenced by the US, this will be reflected
through the lagged market portfolio.